An LMI framework for contraction-based nonlinear control design by derivatives of Gaussian process regression

卷:151

Article

关键词: TRACKING CONTROL;    IDENTIFICATION;    SYSTEMS;    METRICS;    STATE;   

DOI  :  10.1016/j.automatica.2023.110928

来源: SCIE

【 摘 要 】

Contraction theory formulates the analysis of nonlinear systems in terms of Jacobian matrices. Although this provides the potential to develop a linear matrix inequality (LMI) framework for nonlinear control design, conditions are imposed not on controllers but on their partial derivatives, which makes control design challenging. In this paper, we illustrate this so-called integrability problem can be solved by a non-standard use of Gaussian process regression (GPR) for parameterizing controllers and then establish an LMI framework of contraction-based control design for nonlinear discrete-time systems, as an easy-to-implement tool. Later on, we consider the case where the drift vector fields are unknown and employ GPR for functional fitting as its standard use. GPR describes learning errors in terms of probability, and thus we further discuss how to incorporate stochastic learning errors into the proposed LMI framework.(c) 2023 Elsevier Ltd. All rights reserved.

【 授权许可】

Free